Competitive Equilibria: Convergence, Cycles or Chaos
309 Pages Posted: 4 Sep 2003
Date Written: July 2003
There are three types of "Anything Goes" results: two of them from economic theory and one from the realms of dynamical systems. The study considers the implications of such results and tries to identify conditions under which certain types of conclusions may be implied: convergence, cycles or chaos. The study has been divided up into five chapters. Chapters 1 and 2 contain the basic tools of analysis; the first refers to continuous time processes whereas the second refers to discrete time processes. These chapters contain a summary of definitions and results and some applications of these results. The chapters are by no means a comprehensive account of non-linear dynamic systems; they are there to keep the study self-contained. Chapters 3 and 4 contain an analysis of Stability of Competitive Equilibria; the first refers to Walrasian Tatonnement processes while the second to Non-Walrasian or Non-tatonnement processes. We have tried to make the analysis in these chapters as exhaustive as possible, so that readers may understand and appreciate the different aspects of this problem. In short, we examine the workings of the so-called "Invisible Hand" and obtain conditions when the Invisible Hand is also successful in carrying out the tasks that we usually assume that it is capable of. Chapter 5, currently the last chapter, is devoted to processes of economic growth in one sector models. The aspect studied in some detail is the approach to the question of unemployment cycles.
Keywords: Attractors, chaos, closed orbits, convergence, continuous time processes, discrete time processes, dominant diagonals, Dulac's Criterion, cycles, growth, limit sets, Lotka-Volterra Models, non-tatonnement processes, Poincare Bendixson Theorem, stability of equilibrium, stability conditions, tatonnement processes, unemployment cycles, Weak Axiom of Revealed Preference
JEL Classification: C62, C65, D50, D59, E32
Suggested Citation: Suggested Citation